Statistic Methods Encountering Simulations: An Application of the Response Surface Method to the Understanding of RF-MEMS Reconfigurable Power Attenuators

The development of radio frequency (RF) passive components for modern 5G/6G applications, ranging from simple switches to complex network architectures, do often require simulating the system by the finite element method (FEM). FEM is useful when is difficult if not impossible to determine an analytical equation that describes the system of interest starting from the physical laws that describe the phenomena. Therefore, by dividing the complex geometries in a finite number of smaller elements (composing the mesh) physical equations can be easily applied in their analytical form. This approach can be called mechanistic, brutally solves the partial differential equations on each element of the geometry. The overall results are approximated numerical solutions of the problem in which the numerical solution of the single element is passed as input to the bordering elements to build the overall solution of the system. The application on a large number of elements gives an approximate numerical solution in which the relationship with the geometry of the architecture is lost. Using a statistical approach called response surface method (RSM) at the end of a set of simulation, it is possible to partially reconstruct the relationship between the geometrical features and the outcome. Following this approach, we tackled a problem related to radio frequency microelectromechanical system (RF-MEMS) reconfigurable power attenuators. In this specific case, we studied the response of the S21—scattering parameter (attenuation) and the VSWR—voltage standing wave ratio (reflection) to the change of three degrees of freedom (factors), two related to the geometry, and one to the material.